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<div class="titlepage"><div><div><h4 class="title">
<a name="boost_multiprecision.tut.interval.mpfi"></a><a class="link" href="mpfi.html" title="mpfi_float">mpfi_float</a>
</h4></div></div></div>
<p>
          <code class="computeroutput"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">mpfi</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code>
        </p>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span>

<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">mpfi_float_backend</span><span class="special">;</span>

<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="number">50</span><span class="special">&gt;</span> <span class="special">&gt;</span>    <span class="identifier">mpfi_float_50</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="number">100</span><span class="special">&gt;</span> <span class="special">&gt;</span>   <span class="identifier">mpfifloat_100</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="number">500</span><span class="special">&gt;</span> <span class="special">&gt;</span>   <span class="identifier">mpfifloat_500</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="number">1000</span><span class="special">&gt;</span> <span class="special">&gt;</span>  <span class="identifier">mpfi_float_1000</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="number">0</span><span class="special">&gt;</span> <span class="special">&gt;</span>     <span class="identifier">mpfi_float</span><span class="special">;</span>

<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
<p>
          The <code class="computeroutput"><span class="identifier">mpfi_float_backend</span></code>
          type is used in conjunction with <code class="computeroutput"><span class="identifier">number</span></code>:
          It acts as a thin wrapper around the <a href="http://perso.ens-lyon.fr/nathalie.revol/software.html" target="_top">MPFI</a>
          <code class="computeroutput"><span class="identifier">mpfi_t</span></code> to provide an real-number
          type that is a drop-in replacement for the native C++ floating-point types,
          but with much greater precision and implementing interval arithmetic.
        </p>
<p>
          Type <code class="computeroutput"><span class="identifier">mpfi_float_backend</span></code>
          can be used at fixed precision by specifying a non-zero <code class="computeroutput"><span class="identifier">Digits10</span></code>
          template parameter, or at variable precision by setting the template argument
          to zero. The <code class="computeroutput"><span class="keyword">typedef</span></code>s <code class="computeroutput"><span class="identifier">mpfi_float_50</span></code>, <code class="computeroutput"><span class="identifier">mpfi_float_100</span></code>,
          <code class="computeroutput"><span class="identifier">mpfi_float_500</span></code>, <code class="computeroutput"><span class="identifier">mpfi_float_1000</span></code> provide arithmetic types
          at 50, 100, 500 and 1000 decimal digits precision respectively. The <code class="computeroutput"><span class="keyword">typedef</span> <span class="identifier">mpfi_float</span></code>
          provides a variable precision type whose precision can be controlled via
          theF <code class="computeroutput"><span class="identifier">number</span></code>s member functions.
        </p>
<div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/src/images/note.png"></td>
<th align="left">Note</th>
</tr>
<tr><td align="left" valign="top"><p>
            This type only provides <code class="computeroutput"><span class="identifier">numeric_limits</span></code>
            support when the precision is fixed at compile time.
          </p></td></tr>
</table></div>
<p>
          As well as the usual conversions from arithmetic and string types, instances
          of <code class="computeroutput"><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;</span> <span class="special">&gt;</span></code> are copy constructible and assignable
          from:
        </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
              The <a href="http://perso.ens-lyon.fr/nathalie.revol/software.html" target="_top">MPFI</a>
              native type <code class="computeroutput"><span class="identifier">mpfi_t</span></code>.
            </li>
<li class="listitem">
              The <code class="computeroutput"><span class="identifier">number</span></code> wrappers
              around <a href="http://perso.ens-lyon.fr/nathalie.revol/software.html" target="_top">MPFI</a>
              or <a href="http://www.mpfr.org" target="_top">MPFR</a>: <code class="computeroutput"><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="identifier">M</span><span class="special">&gt;</span> <span class="special">&gt;</span></code>
              and <code class="computeroutput"><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfr_float</span><span class="special">&lt;</span><span class="identifier">M</span><span class="special">&gt;</span> <span class="special">&gt;</span></code>.
            </li>
<li class="listitem">
              There is a two argument constructor taking two <code class="computeroutput"><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfr_float</span><span class="special">&lt;</span><span class="identifier">M</span><span class="special">&gt;</span> <span class="special">&gt;</span></code>
              arguments specifying the interval.
            </li>
</ul></div>
<p>
          It's also possible to access the underlying <code class="computeroutput"><span class="identifier">mpfi_t</span></code>
          via the <code class="computeroutput"><span class="identifier">data</span><span class="special">()</span></code>
          member function of <code class="computeroutput"><span class="identifier">mpfi_float_backend</span></code>.
        </p>
<p>
          Things you should know when using this type:
        </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
              A default constructed <code class="computeroutput"><span class="identifier">mpfi_float_backend</span></code>
              is set to zero (<span class="emphasis"><em>Note that this is <span class="bold"><strong>not</strong></span>
              the default <a href="http://perso.ens-lyon.fr/nathalie.revol/software.html" target="_top">MPFI</a>
              behavior</em></span>).
            </li>
<li class="listitem">
              No changes are made to <a href="http://gmplib.org" target="_top">GMP</a> or
              <a href="http://www.mpfr.org" target="_top">MPFR</a> global settings, so this
              type can coexist with existing <a href="http://www.mpfr.org" target="_top">MPFR</a>
              or <a href="http://gmplib.org" target="_top">GMP</a> code.
            </li>
<li class="listitem">
              The code can equally use <a href="http://mpir.org/" target="_top">MPIR</a>
              in place of <a href="http://gmplib.org" target="_top">GMP</a> - indeed that
              is the preferred option on Win32.
            </li>
<li class="listitem">
              This backend supports rvalue-references and is move-aware, making instantiations
              of <code class="computeroutput"><span class="identifier">number</span></code> on this backend
              move aware.
            </li>
<li class="listitem">
              Conversion from a string results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code>
              being thrown if the string can not be interpreted as a valid floating-point
              number.
            </li>
<li class="listitem">
              Division by zero results in an infinity.
            </li>
</ul></div>
<p>
          There are some additional non member functions for working on intervals:
        </p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;</span>
<span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfr_float_backend</span><span class="special">&lt;</span><span class="identifier">Digits10</span><span class="special">&gt;,</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;</span> <span class="identifier">lower</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="identifier">Digits10</span><span class="special">&gt;,</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;&amp;</span> <span class="identifier">val</span><span class="special">);</span>
</pre>
<p>
          Returns the lower end of the interval.
        </p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;</span>
<span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfr_float_backend</span><span class="special">&lt;</span><span class="identifier">Digits10</span><span class="special">&gt;,</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;</span> <span class="identifier">upper</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="identifier">Digits10</span><span class="special">&gt;,</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;&amp;</span> <span class="identifier">val</span><span class="special">);</span>
</pre>
<p>
          Returns the upper end of the interval.
        </p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;</span>
<span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfr_float_backend</span><span class="special">&lt;</span><span class="identifier">Digits10</span><span class="special">&gt;,</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;</span> <span class="identifier">median</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="identifier">Digits10</span><span class="special">&gt;,</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;&amp;</span> <span class="identifier">val</span><span class="special">);</span>
</pre>
<p>
          Returns the mid point of the interval.
        </p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;</span>
<span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfr_float_backend</span><span class="special">&lt;</span><span class="identifier">Digits10</span><span class="special">&gt;,</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;</span> <span class="identifier">width</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="identifier">Digits10</span><span class="special">&gt;,</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;&amp;</span> <span class="identifier">val</span><span class="special">);</span>
</pre>
<p>
          Returns the absolute width of the interval.
        </p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;</span>
<span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="identifier">Digits10</span><span class="special">&gt;,</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;</span> <span class="identifier">intersect</span><span class="special">(</span>
  <span class="keyword">const</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="identifier">Digits10</span><span class="special">&gt;,</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;&amp;</span> <span class="identifier">a</span><span class="special">,</span>
  <span class="keyword">const</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="identifier">Digits10</span><span class="special">&gt;,</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;&amp;</span>  <span class="identifier">b</span><span class="special">);</span>
</pre>
<p>
          Returns the interval which is the intersection of the <span class="emphasis"><em>a</em></span>
          and <span class="emphasis"><em>b</em></span>. Returns an unspecified empty interval if there
          is no such intersection.
        </p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;</span>
<span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="identifier">Digits10</span><span class="special">&gt;,</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;</span> <span class="identifier">hull</span><span class="special">(</span>
  <span class="keyword">const</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="identifier">Digits10</span><span class="special">&gt;,</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;&amp;</span> <span class="identifier">a</span><span class="special">,</span>
  <span class="keyword">const</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="identifier">Digits10</span><span class="special">&gt;,</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;&amp;</span>  <span class="identifier">b</span><span class="special">);</span>
</pre>
<p>
          Returns the interval which is the union of <span class="emphasis"><em>a</em></span> and
          <span class="emphasis"><em>b</em></span>.
        </p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;</span>
<span class="keyword">bool</span> <span class="identifier">overlap</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="identifier">Digits10</span><span class="special">&gt;,</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;&amp;</span> <span class="identifier">a</span><span class="special">,</span>
             <span class="keyword">const</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="identifier">Digits10</span><span class="special">&gt;,</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;&amp;</span>  <span class="identifier">b</span><span class="special">);</span>
</pre>
<p>
          Returns <code class="computeroutput"><span class="keyword">true</span></code> only if the intervals
          <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span> overlap.
        </p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates1</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates2</span><span class="special">&gt;</span>
<span class="keyword">bool</span> <span class="identifier">in</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfr_float_backend</span><span class="special">&lt;</span><span class="identifier">Digits10</span><span class="special">&gt;,</span> <span class="identifier">ExpressionTemplates1</span><span class="special">&gt;&amp;</span> <span class="identifier">a</span><span class="special">,</span>
        <span class="keyword">const</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="identifier">Digits10</span><span class="special">&gt;,</span> <span class="identifier">ExpressionTemplates2</span><span class="special">&gt;&amp;</span>  <span class="identifier">b</span><span class="special">);</span>
</pre>
<p>
          Returns <code class="computeroutput"><span class="keyword">true</span></code> only if point
          <span class="emphasis"><em>a</em></span> is contained within the interval <span class="emphasis"><em>b</em></span>.
        </p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;</span>
<span class="keyword">bool</span> <span class="identifier">zero_in</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="identifier">Digits10</span><span class="special">&gt;,</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;&amp;</span> <span class="identifier">a</span><span class="special">);</span>
</pre>
<p>
          Returns <code class="computeroutput"><span class="keyword">true</span></code> only if the interval
          <span class="emphasis"><em>a</em></span> contains the value zero.
        </p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;</span>
<span class="keyword">bool</span> <span class="identifier">subset</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="identifier">Digits10</span><span class="special">&gt;,</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;&amp;</span> <span class="identifier">a</span><span class="special">,</span>
            <span class="keyword">const</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="identifier">Digits10</span><span class="special">&gt;,</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;&amp;</span> <span class="identifier">b</span><span class="special">);</span>
</pre>
<p>
          Returns <code class="computeroutput"><span class="keyword">true</span></code> only if <span class="emphasis"><em>a</em></span>
          is a subset of <span class="emphasis"><em>b</em></span>.
        </p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;</span>
<span class="keyword">bool</span> <span class="identifier">proper_subset</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="identifier">Digits10</span><span class="special">&gt;,</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;&amp;</span> <span class="identifier">a</span><span class="special">,</span>
                   <span class="keyword">const</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="identifier">Digits10</span><span class="special">&gt;,</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;&amp;</span> <span class="identifier">b</span><span class="special">);</span>
</pre>
<p>
          Returns <code class="computeroutput"><span class="keyword">true</span></code> only if <span class="emphasis"><em>a</em></span>
          is a proper subset of <span class="emphasis"><em>b</em></span>.
        </p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;</span>
<span class="keyword">bool</span> <span class="identifier">empty</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="identifier">Digits10</span><span class="special">&gt;,</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;&amp;</span> <span class="identifier">a</span><span class="special">);</span>
</pre>
<p>
          Returns <code class="computeroutput"><span class="keyword">true</span></code> only if <span class="emphasis"><em>a</em></span>
          is an empty interval, equivalent to <code class="computeroutput"><span class="identifier">upper</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span>
          <span class="special">&lt;</span> <span class="identifier">lower</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span></code>.
        </p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;</span>
<span class="keyword">bool</span> <span class="identifier">singleton</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="identifier">Digits10</span><span class="special">&gt;,</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;&amp;</span> <span class="identifier">a</span><span class="special">);</span>
</pre>
<p>
          Returns <code class="computeroutput"><span class="keyword">true</span></code> if <code class="computeroutput"><span class="identifier">lower</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span> <span class="special">==</span>
          <span class="identifier">upper</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span></code>.
        </p>
<h6>
<a name="boost_multiprecision.tut.interval.mpfi.h0"></a>
          <span class="phrase"><a name="boost_multiprecision.tut.interval.mpfi.mpfi_example"></a></span><a class="link" href="mpfi.html#boost_multiprecision.tut.interval.mpfi.mpfi_example"> MPFI
          example:</a>
        </h6>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">mpfi</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>

<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
<span class="special">{</span>
   <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span>

   <span class="comment">// Operations at variable precision and no numeric_limits support:</span>
   <span class="identifier">mpfi_float</span> <span class="identifier">a</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span>
   <span class="identifier">mpfi_float</span><span class="special">::</span><span class="identifier">default_precision</span><span class="special">(</span><span class="number">1000</span><span class="special">);</span>
   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">mpfi_float</span><span class="special">::</span><span class="identifier">default_precision</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// print root-2</span>

   <span class="comment">// Operations at fixed precision and full numeric_limits support:</span>
   <span class="identifier">mpfi_float_100</span> <span class="identifier">b</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span>
   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">mpfi_float_100</span><span class="special">&gt;::</span><span class="identifier">digits</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
   <span class="comment">// We can use any C++ std lib function:</span>
   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">log</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// print log(2)</span>

   <span class="comment">// Access the underlying data:</span>
   <span class="identifier">mpfi_t</span> <span class="identifier">r</span><span class="special">;</span>
   <span class="identifier">mpfi_init</span><span class="special">(</span><span class="identifier">r</span><span class="special">);</span>
   <span class="identifier">mpfi_set</span><span class="special">(</span><span class="identifier">r</span><span class="special">,</span> <span class="identifier">b</span><span class="special">.</span><span class="identifier">backend</span><span class="special">().</span><span class="identifier">data</span><span class="special">());</span>

   <span class="comment">// Construct some explicit intervals and perform set operations:</span>
   <span class="identifier">mpfi_float_50</span> <span class="identifier">i1</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="number">2</span><span class="special">),</span> <span class="identifier">i2</span><span class="special">(</span><span class="number">1.5</span><span class="special">,</span> <span class="number">2.5</span><span class="special">);</span>
   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">intersect</span><span class="special">(</span><span class="identifier">i1</span><span class="special">,</span> <span class="identifier">i2</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">hull</span><span class="special">(</span><span class="identifier">i1</span><span class="special">,</span> <span class="identifier">i2</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">overlap</span><span class="special">(</span><span class="identifier">i1</span><span class="special">,</span> <span class="identifier">i2</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">subset</span><span class="special">(</span><span class="identifier">i1</span><span class="special">,</span> <span class="identifier">i2</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
   <span class="identifier">mpfi_clear</span><span class="special">(</span><span class="identifier">r</span><span class="special">);</span>
   <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
<span class="special">}</span>
</pre>
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      Maddock and Christopher Kormanyos<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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